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A051452 a(n) = 1 + lcm(1..k) where k is the n-th prime power A000961(n).

%I A051452 #31 Aug 15 2024 08:18:43
%S A051452 2,3,7,13,61,421,841,2521,27721,360361,720721,12252241,232792561,
%T A051452 5354228881,26771144401,80313433201,2329089562801,72201776446801,
%U A051452 144403552893601,5342931457063201,219060189739591201
%N A051452 a(n) = 1 + lcm(1..k) where k is the n-th prime power A000961(n).
%C A051452 From _Daniel Forgues_, Apr 27 2014: (Start)
%C A051452 Factorizations:
%C A051452   2, 3, 7, 13, 61, 421 are primes;
%C A051452   841 = 29^2;
%C A051452   2521 is prime;
%C A051452   27721 = 19*1459, 360361 = 89*4049, 720721 = 71*10151,
%C A051452   12252241 = 1693*7237;
%C A051452   232792561 is prime;
%C A051452   5354228881 = 6659*804059;
%C A051452   26771144401 is prime;
%C A051452   80313433201 = 331*11239*21589, 2329089562801 = 101*271*2311*36821;
%C A051452   72201776446801 is prime.
%C A051452 Very likely contains an infinite number of primes (see A049536). (End)
%o A051452 (PARI) print1(2);t=1;for(n=2,100,if(t%n, t=lcm(t,n); print1(", "t+1))) \\ _Charles R Greathouse IV_, Jan 04 2013
%o A051452 (Python)
%o A051452 from math import prod
%o A051452 from sympy import primepi, integer_nthroot, integer_log, primerange
%o A051452 def A051452(n):
%o A051452     def f(x): return int(n+x-1-sum(primepi(integer_nthroot(x,k)[0]) for k in range(1,x.bit_length())))
%o A051452     m, k = n, f(n)
%o A051452     while m != k:
%o A051452         m, k = k, f(k)
%o A051452     return 1+prod(p**integer_log(m, p)[0] for p in primerange(m+1)) # _Chai Wah Wu_, Aug 15 2024
%Y A051452 1 + A003418(A000961(n)), corresponds to distinct values of 1 + A003418.
%Y A051452 Cf. A049536, A049537, A051454, A208768.
%K A051452 nonn
%O A051452 1,1
%A A051452 _Labos Elemer_